This invention relates to imaging, and more particularly, to the high speed reprojection of tomographic images.
Tomographic images are created from line integral measurements of an unknown object at a variety of orientations. These line integral measurements, which may represent measurements of density, reflectivity, etc., are then processed to yield an image that represents the unknown object. Data generated in this manner is collected into a sinogram, and the sinogram is processed and backprojected to create the image. Tomographic reconstruction is the technique underlying nearly all of the key diagnostic S imaging modalities including X-ray Computed Tomography (CT), Positron Emission Tomography (PET), Single Photon Emission Count Tomography (SPECT), certain acquisition methods for Magnetic Resonance Imaging (MRI), and newly emerging techniques such as electrical impedance tomography (EIT) and optical tomography,
The process of reprojection simulates a tomographic data acquisition system. Reprojection is generally used in two contexts. The first is in artifact correction. Here, reprojection is used to simulate the data acquisition procedure on a candidate reconstructed image. Differences between the reprojected image and the measured data can then be used to correct for mismodeling. Second, reprojection can be used in iterative reconstruction algorithms. For these algorithms, the reconstruction process is done via iteration, involving a number of computationally intensive steps, generally dominated by reprojection and backprojection. These iterations require substantial computing resources, including hardware allocation and processing time, and are therefore expensive. Thus, fast methods for backprojection need to be coupled with fast methods for reprojection to provide an overall speedup in such methods.
Accordingly, one object of this invention is to provide new and improved methods for imaging.
Another object is to provide methods for reprojection which provide an overall speedup and reduction of computational cost.
In keeping with one aspect of this invention, a method for reprojecting sinograms includes the steps of dividing a two-dimensional image into sub-images as small as on pixel, and reprojecting the sub-images at a smaller number of orientations to form subsinograms. These sub-sinograms are then successively aggregated and processed to form a full sinogram.
The method uses two algorithms to aggregate the sub-sinograms. In one algorithm, aggregation is exact, and in the other algorithm, aggregation is an approximation. The first algorithm is accurate, but relatively slow, and the second algorithm is faster, but less accurate. By performing some aggregations with the exact algorithm and some aggregations with the approximate algorithm, switching between the two algorithms in any of a number of suitable ways, an accurate result can be obtained quickly.